c1*cos(3*x)-3*x*cos(3*x)+ ... x))+c2*sin(3*x) если x=-2 (упростите выражение)

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Решение

Вы ввели [src]
c1*cos(3*x) - 3*x*cos(3*x) + sin(3*x)*log(sin(3*x)) + c2*sin(3*x)
$$c_{2} \sin{\left (3 x \right )} + c_{1} \cos{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Подстановка условия [src]
c1*cos(3*x) - 3*x*cos(3*x) + sin(3*x)*log(sin(3*x)) + c2*sin(3*x) при x = -2
c1*cos(3*x) - 3*x*cos(3*x) + sin(3*x)*log(sin(3*x)) + c2*sin(3*x)
$$c_{2} \sin{\left (3 x \right )} + c_{1} \cos{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
c1*cos(3*(-2)) - 3*(-2)*cos(3*(-2)) + sin(3*(-2))*log(sin(3*(-2))) + c2*sin(3*(-2))
$$c_{2} \sin{\left (3 (-2) \right )} + - 3 (-2) \cos{\left (3 (-2) \right )} + c_{1} \cos{\left (3 (-2) \right )} + \log{\left (\sin{\left (3 (-2) \right )} \right )} \sin{\left (3 (-2) \right )}$$
c1*cos(3*(-2)) - 3*(-2)*cos(3*(-2)) + sin(3*(-2))*log(sin(3*(-2))) + c2*sin(3*(-2))
$$c_{2} \sin{\left (-2 \cdot 3 \right )} + c_{1} \cos{\left (-2 \cdot 3 \right )} - - 6 \cos{\left (-2 \cdot 3 \right )} + \log{\left (\sin{\left (-2 \cdot 3 \right )} \right )} \sin{\left (-2 \cdot 3 \right )}$$
6*cos(6) + c1*cos(6) - c2*sin(6) - log(-sin(6))*sin(6)
$$c_{1} \cos{\left (6 \right )} - c_{2} \sin{\left (6 \right )} - \log{\left (- \sin{\left (6 \right )} \right )} \sin{\left (6 \right )} + 6 \cos{\left (6 \right )}$$
Степени [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Численный ответ [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3.0*x*cos(3*x)
Рациональный знаменатель [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Объединение рациональных выражений [src]
c2*sin(3*x) + (c1 - 3*x)*cos(3*x) + log(sin(3*x))*sin(3*x)
$$c_{2} \sin{\left (3 x \right )} + \left(c_{1} - 3 x\right) \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Общее упрощение [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Собрать выражение [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
c1*cos(3*x) + c2*sin(3*x) + sin(3*x)*log(sin(3*x)) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
(c1 - 3*x)*cos(3*x) + (c2 + log(sin(3*x)))*sin(3*x)
$$\left(c_{1} - 3 x\right) \cos{\left (3 x \right )} + \left(c_{2} + \log{\left (\sin{\left (3 x \right )} \right )}\right) \sin{\left (3 x \right )}$$
Общий знаменатель [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Тригонометрическая часть [src]
c2*sin(3*x) + (c1 - 3*x)*cos(3*x) + log(sin(3*x))*sin(3*x)
$$c_{2} \sin{\left (3 x \right )} + \left(c_{1} - 3 x\right) \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Комбинаторика [src]
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$
Раскрыть выражение [src]
   /   3           2          \      /     3           2          \   /     3           2          \    /     3           2          \       /   3           2          \
c1*\cos (x) - 3*sin (x)*cos(x)/ + c2*\- sin (x) + 3*cos (x)*sin(x)/ + \- sin (x) + 3*cos (x)*sin(x)/*log\- sin (x) + 3*cos (x)*sin(x)/ - 3*x*\cos (x) - 3*sin (x)*cos(x)/
$$c_{1} \left(- 3 \sin^{2}{\left (x \right )} \cos{\left (x \right )} + \cos^{3}{\left (x \right )}\right) + c_{2} \left(- \sin^{3}{\left (x \right )} + 3 \sin{\left (x \right )} \cos^{2}{\left (x \right )}\right) - 3 x \left(- 3 \sin^{2}{\left (x \right )} \cos{\left (x \right )} + \cos^{3}{\left (x \right )}\right) + \left(- \sin^{3}{\left (x \right )} + 3 \sin{\left (x \right )} \cos^{2}{\left (x \right )}\right) \log{\left (- \sin^{3}{\left (x \right )} + 3 \sin{\left (x \right )} \cos^{2}{\left (x \right )} \right )}$$
c1*cos(3*x) + c2*sin(3*x) + log(sin(3*x))*sin(3*x) - 3*x*cos(3*x)
$$c_{1} \cos{\left (3 x \right )} + c_{2} \sin{\left (3 x \right )} - 3 x \cos{\left (3 x \right )} + \log{\left (\sin{\left (3 x \right )} \right )} \sin{\left (3 x \right )}$$